Wavelet Sampling and Localization Schemes for the Radon Transform in Two Dimensions

Two theorems are presented for wavelet decompositions of the two-dimensional Radon transform. The first theorem establishes an upper error bound in L-norm between the Radon transform and its wavelet approximation whose coefficients at different scales are estimated from Radon data acquired at corresponding sampling rates. The second theorem gives an estimate of the accuracy of a local image reconstructed from localized Radon data at multiple levels. These results show how to design a multilevel sampling and localization strategy for parallel-beam scanning by using wavelet regularity and vanishing moment characteristics, clarify the interaction between the wavelet structure and the essential bandwidth of an object image, and provide guidelines for wavelet local tomography.